Question

Alpha and beta are the zeros of the polynomial 5x^2+x-3 find the value of alpha square - beta square

Answer 1

5x^2+x-3=0

a and b are root

so for a^2-b^2=(a+b)(a-b)

a+b=-1/5

and for (a-b)

we know (a-b)^2=(a+b)^2-4ab

and a+b=-1/5

and ab=-3/5

so (a-b)^2=(a+b)^2-4ab

(a-b)^2=( -1/5)^2-4(-3/5)

(a-b)^2=61/25

(a-b)=√61/5

so a^2-b^2=( -1/5)×√61/5

anser is -√61/25.

Hope these will help you.